What to do when leveling

[Avenger]

Is it worth it to try to craft whatever "maxed" gear is for the base game/expansions for crafting? Or should I just speed through it?

I'm not entirely what you're asking, but I can say that the max HQ crafted gear, currently i380, is upgradable to i390 and is definitely useful at lv70.

If you're asking about leveling gear, you burn through it so quickly that frequent upgrades seem like a waste of time (and possibly gil and/or materia.) NQ gear is also fine for leveling.
For several dps and healer jobs I ignored crafted leveling gear almost entirely from 50-69 and used tomestone gear (ARR/i130/ironworks and HW/i260/shire) instead.

Beast Tribe Quests: I don't think the ARR beast tribe quests are necessary if you don't care about their rewards, but they may have some purpose that I'm unaware of.

Glamours: I don't know of a good web site for glamours (though for gear and melding I recommend ffxiv.ariyala.com). I wish FFXIV had a system more like GW2!! Putting an item in the glamour closet doesn't cost anything, but applying a glamour to an item uses a glamour prism.

Leveling: I am not a leveling fiend, but I do have some thoughts. The fastest path from 1-60 might be to purchase a skip potion, but I don't recommend it since leveling is fast and fun. The fastest way to get to lv50 is to be a RDM or a SAM, which start at lv50. However, XP rains from the skies these days, so leveling from 1 to 50 isn't bad; I usually equip an XP item if possible (such as allagan earring which gives 30% to lv70), use the rested bonus on my highest-level job, run roulettes, complete my hunt log, run challenge log, beast tribe quests, etc.. Guildhests also give bonus XP the first time you do them and also count toward a challenge log. Even FATE grinding still works - I leveled up a bunch while I was grinding FATES for the hellish Yo-kai event. From 50 onward, Alliance Raid Roulette seems to give a lot of XP, and regular hunt marks also give XP. Many people still level via Palace of the Dead, which has the nice property that you don't need to worry about gear – and you get other rewards too. From 60-70 I really appreciate the beast tribe quests as a bonus XP source. And last (but not least!) at-level dungeons give a lot of XP!! More so if you stack rested and other bonuses.

[Ha, now that I'm writing this I want to log on and level a bit!]

Oh, and until they fix it in 5.0 you can cheat by having people power-level you in the overworld by killing enemies that you tag - I believe you get full XP even if a lv70 char kills it. This seems like it might not be much fun, but they announced that they aren't going to fix it until 5.0 and they won't ban you for doing it. Apparently it's been this way for a long time, but it's particularly apparent now with BLU, which uses overworld leveling and gets crazy bonus XP.